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    Lifetime of Surface Bubbles in Surfactant Solutions
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    • Omer Atasi*
      Omer Atasi
      Transfers, Interfaces and Processes, Université Libre de Bruxelles, Brussels 1050, Belgium
      Institut de Mécanique des Fluides de Toulouse (IMFT), Université de Toulouse, CNRS, Toulouse, France
      Soft Matter, Fluidics and Interfaces, MESA+ Institute for Nanotechnology, University of Twente, Enschede, The Netherlands
      *Email: [email protected]
      More by Omer Atasi
      Orcidhttp://orcid.org/0000-0003-4957-3996
    • Dominique Legendre
      Dominique Legendre
      Institut de Mécanique des Fluides de Toulouse (IMFT), Université de Toulouse, CNRS, Toulouse, France
      More by Dominique Legendre
    • Benoit Haut
      Benoit Haut
      Transfers, Interfaces and Processes, Université Libre de Bruxelles, Brussels 1050, Belgium
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    • Roberto Zenit
      Roberto Zenit
      Center for Fluid Mechanics, School of Engineering, Brown University, 184 Hope Street, Providence, Rhode Island 02912, United States
      More by Roberto Zenit
    • Benoit Scheid
      Benoit Scheid
      Transfers, Interfaces and Processes, Université Libre de Bruxelles, Brussels 1050, Belgium
      More by Benoit Scheid
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    Langmuir

    Cite this: Langmuir 2020, 36, 27, 7749–7764
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    https://doi.org/10.1021/acs.langmuir.9b03597
    Published June 8, 2020
    Copyright © 2020 American Chemical Society
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    Abstract

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    Despite the prevalence of surface bubbles in many natural phenomena and engineering applications, the effect of surfactants on their surface residence time is not clear. Numerous experimental studies and theoretical models exist but a clear understanding of the film drainage phenomena is still lacking. In particular, theoretical work predicting the drainage rate of the thin film between a bubble and the free surface in the presence and absence of surfactants usually makes use of the lubrication theory. On the other hand, in numerous natural situations and experimental works, the bubble approaches the free surface from a certain distance and forms a thin film at a later stage. This article attempts to bridge these two approaches. In particular, in this article, we review these works and compare them to our direct numerical simulations where we study the coupled influence of bubble deformation and surfactants on the rising and drainage process of a bubble beneath a free surface. In the present study, the level-set method is used to capture the air–liquid interfaces, and the transport equation of surfactants is solved in an Eulerian framework. The axisymmetric simulations capture the bubble acceleration, deformation, and rest (or drainage) phases from nondeformable to deformable bubbles, as measured by the Bond number (Bo), and from surfactant-free to surfactant-coated bubbles, as measured by the Langmuir number (La). The results show that the distance h between the bubble and the free surface decays exponentially for surfactant-free interfaces (La = 0), and this decay is faster for nondeformable bubbles (Bo ≪ 1) than for deformable ones (Bo ≫ 1). The presence of surfactants (La > 0) slows the decay of h, exponentially for large bubbles (Bo ≫ 1) and algebraically for small ones (Bo ≪ 1). For Bo ≈ 1, the lifetime is the longest and is associated with the (Marangoni) elasticity of the interfaces.

    Copyright © 2020 American Chemical Society

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    Langmuir

    Cite this: Langmuir 2020, 36, 27, 7749–7764
    Click to copy citationCitation copied!
    https://doi.org/10.1021/acs.langmuir.9b03597
    Published June 8, 2020
    Copyright © 2020 American Chemical Society
    Request reuse permissions

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